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Apps for Mathematics Learning: A Review of 'Educational' Apps from the iTunes App Store Kate Highfield Kristy Goodwin Chance to L~am Increasingly iPads1M are being used in schools and prior-to-school settings, with a plethora of Apps available for mathematics learning. Despite the growing number of Apps available in the iTunes App Store, there has been limited systematic analysis of the pedagogic design of Apps designed for mathematics learning. This paper describes a content analysis of Apps that are currently available as 'educational' content in the iTunes App Store and highlights the limited range of pedagogic designs available for mathematics learning. Increasingly mobile touch devices, such as the iPhone, iPod touch and iPads, are suggested as tools for mathematics learning (McKenna, 2012). This is particularly relevant in the early years of schooling where teachers perceive these as valid pedagogical devices (Olney, Herrington, & Verenikina, 2008) that are engaging for learners (McKenna, 2012). In part, this is because these devices compensate for the fine motor skills required to operate traditional computers with a mouse. Here we see that the direct touch interface and gestural actions allow children to easily manipulate and interact with screen objects and create digital content. Further, the mobile nature of these devices affords cost-effective use in multiple contexts, rather than in just one curriculum area (Aronin & Floyd, 2013) or in a computer laboratory or fiXed position in the classroom. The Michael Cohen Group LLC (20 II) suggests that some Apps designed for use on these devices allow young children to learn and discover in ways that are commensurate with their preferred learning modes: physical touch, trial and error, and repetition. These attributes, combined with the relatively low cost options available, appear to make touch devices an appealing platform and may account for educators' increasing embrace of these technologies. Background Whilst there is emerging research examining the effectiveness of mobile Apps (PBS Kids, 2010, Shuler, 2009), much of the research has been conducted by large media organisations or focuses on case study trials of devices. In mathematics education there is limited, but growing corpus of research outlining the use of Apps and accompanying pedagogies. However, studies examining these tools in mathematics education are beginning to highlight the potential of specific Apps for learning or examine integration of these technologies (Aronin & Floyd, 2013; Attard & Curry, 2012; Kiger, Herro & Prunty, 2012; McKenna, 2012). Despite the limited research, these devices can be seen to afford visual representations that are essential for communicating ideas and concepts (Goldin & Kaput, 1996). Further, as with other technologies, these tools offer new affordances for representation (Highfield & Mulligan, 2007; Moyer, Niezgoda & Stanley, 2005) and engagement in dynamic representations (Goodwin, 2009). A content analysis of the App store shows that a significant proportion of the top 100-selling Apps (for iPhone and iPod touch devices) in the United States are designed for preschool or primary aged children. This analysis by Shuler's (2009) found that 47% of most popular Apps are designed for these age groups. Shuler's (2009) analysis, consistent with the later work of Watlington (20 II), found that foreign language and literacy the most In V. Steinle, L. Ball & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th aonual conference of the Mathematics Edueation Research Group of Aus1ralasia). Melbourne, VIC: MERGA. Cl Mathematics Edueation Research Group of Aus1ralasia Inc. 2013 378 MERGA36 - 2013 Mathematics Education: Yesterday, Today and Tomorrow Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia KEYNOTES AUTHORS TITLE PAGE Brian Butterworth The Mathematical Brain and Numeracy (abstract) 1 Yoshinori Shimizu Working at the Intersection of Research and Practice: A Perspective on the Study and Improvement of Mathematics Lessons 2 Kaye Stacey Bringing Research on Students Understanding into the Classroom through Formative Assessment 13 Gloria Stillman Annual Clements Foyster Lecture: Problem Finding, Problem Posing, Problem Solving: Mathematics Education Research - Yesterday, Today, Tomorrow (abstract) 22 PRACTICAL IMPLICATIONS AWARD Peter Gould Changes in Students Notation When Fractions Exceed One-Whole 25 RESEARCH PAPERS Probing Students' Numerical Misconceptions in School Algebra 36 Zarina Akhtar & Vicki Steinle Mapping Students' Spoken Conceptions of Equality 44 Megan Anakin Mathematics Teachers Perceptions of their Students Mathematical Competence: Relations to Mathematics Achievement, Affect, and Engagement in Singapore and Australia 52 Shaljan Areepattamannil & Berinderjeet Kaur Integrating iPads into Primary Mathematics Pedagogies: An Exploration of Two Teachers' Experiences 58 Catherine Attard Respectful and Responsive Pedagogies for Mathematics and Statistics 66 Robin Averill & Megan Clarke Using a Modified Form of Lesson Study to Develop Students' Relational Thinking in Years 4, 5 & 6 74 Lei Bao & Max Stephens Technology Prompts New Understandings: The Case of Equality 82 Caroline Bardini, Reinhard Oldenburg, Kaye Stacey & Robyn Pierce Teacher Identity and Numeracy: Developing an Analytic Lens for Understanding Numeracy Teacher Identity 90 Anne Bennison & Merrilyn Goos Translation of Data from a Real-life Context into Graphical Representations 98 Casandra Blagdanic & Mohan Chinnappan Teaching Roles in Technology-Rich Teaching and Learning Environments (TRTLE's) 106 Jill Brown Identification of Hierarchies of Student Learning about Percentages using Rasch Analysis 114 Joan Burfitt Use of Learning Trajectories to Examine Pre-service Teachers Mathematics Knowledge for Teaching Area and Perimeter: 122 Barbara Butterfield, Tricia Forrester, Faye McCallum & Mohan Chinnappan Gender Differences in Children's Mathematics Achievement: Perspectives from the Longitudinal Study of Australian Children 130 Colin Carmichael Relationship Between Mathematics Anxiety and Attitude Towards Mathematics among Indian Students 138 Mini Chaman & Rosemary Callingham Using Photographs and Diagrams to Test Young Childrens Mass Thinking 146 Jill Cheeseman & Andrea McDonough Teachers Views of the Challenging Elements of a Task 154 Jill Cheeseman, Doug Clarke, Anne Roche & Karen Wilson Posing Problems to Understand Children's Learning of Fractions 162 Lu Pien Cheng Educating Boris: An Examination of Pedagogical Content Knowledge for Mathematics Teacher Educators 170 Helen Chick & Kim Beswick Translating Between and Within Representations: Mathematics As Lived Experiences and Interactions 178 Philemon Chigeza Productive Mathematical Noticing: What It Is and Why It Matters 186 Ban Heng Choy Designing Tasks to Promote and Assess Mathematical Transfer in Primary School Children 194 Julie Clark, Shaileigh Page & Steve Thornton Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students: An Early Report 202 Tom Cooper, David Nutchey & Edlyn Grant Thoughts Behind the Actions: Exploring Preservice Teachers' Mathematical Content Knowledge 210 Leah Daniel & Josephine Balatti Sticking With It or Doing It Quickly: What Performances Do We Encourage In Our Mathematics Learners? 218 Lisa Darragh Pre-service Secondary Mathematics Teachers Reflections on Good and Bad Mathematics Teaching 226 Hem Dayal When Practice Doesn't Lead to Retrieval: An Analysis of Children's Errors with Simple Addition 234 Celeste de Villiers & Sarah Hopkins Making Connections Between Multiplication and Division 242 Ann Downton How Heavy is my Rock? An Exploration of Students' Understanding of the Measurement of Weight 250 Michael Drake How Do Adults Perceive, Analyse and Measure Slope? 258 Bruce Duncan & Helen Chick Great Expectations: Teaching Mathematics in English to Indigenous Language Speaking Students 266 Cris Edmonds-Wathen Beginning Inference in Fourth Grade: Exploring Variation in Measurement 274 Lyn English & Jane Watson Scaffolding the Mathematics Learning of Low-attaining Students Through Whole Class Discussions 282 Sarah Ferguson Inquiry-Based Argumentation in Primary Mathematics: Reflecting on Evidence 290 Jill Fielding-Wells The Make it Count Project: NAPLAN Achievement Evaluation 298 Helen Forgasz, Gilah Leder & Jennifer Halliday Students 'Holding' the Moment: Learning Mathematics in an Inquiry Mathematics Classroom 306 Kym Fry Students and Real World Applications: Still a Challenging Mix 314 Peter Galbraith Students Using Digital Technologies to Produce Screencasts That Support Learning in Mathematics 322 Linda Galligan & Carola Hobohm Exploring the Demands and Opportunities for Numeracy in the Australian Curriculum: English 330 Vince Geiger, Merrilyn Goos, Shelley Dole, Helen Forgasz & Anne Bennison Children's Mathematical Knowledge Prior to Starting School 338 Ann Gervasoni & Bob Perry Longitudinal Progress of 6-year-old Students Who Participated in an Extending Mathematical Understanding Mathematics Intervention Program 346 Ann Gervasoni, Linda Parish, Carole Livesey, Melissa Croswell, Kate Bevan, Teresa Hadden & Kathie Turkenburg Measuring Mathematics Teacher Educators' Knowledge of Technology Integrated Teaching: Instrument Development 354 Seyum Tekeher Getenet & Kim Beswick Principals' Views on the Importance of Numeracy as Children Start Primary School 362 Wendy Goff, Sue Dockett & Bob Perry Mathematics Education as a Practice: A Theoretical Position 370 Peter Grootenboer & Christine Edwards-Groves Apps for Mathematics Learning: A Review of 'Educational' Apps from the iTunes App Store 378 Kate Highfield & Kristy Goodwin What Teachers See When Watching Others Teach 386 Louise Hodgson Pre-service Primary Teachers Choice of Mathematical Examples: Formative Analysis of Lesson Plan Data 394 Ray Huntley Mathematical Engagement Skills 402 Naomi Ingram Early-Years Swimming: Creating Opportunities for Adding Mathematical Capital to Under 5 410 Robyn Jorgensen Relationships of Out-of-School-Time Mathematics Lessons to Mathematical Literacy in Singapore and Australia 418 Berinderjeet Kaur & Shaljan Areepattamannil Maths Education: Is There An App For That? 426 Kevin Larkin Transactional Distance Theory (TDT): An Approach to Enhancing Knowledge and Reducing Anxiety of Pre-Service Teachers Studying a Mathematics Education Course Online 434 Kevin Larkin & Romina Jamieson-Proctor Foundation Content Knowledge: What Do Pre-Service Teachers Need To Know? 442 Chris Linsell & Megan Anakin Pre-service Teachers' Responses for Ratio and Proportion Items 450 Sharyn Livy & Sandra Herbert From Curriculum to Workplace Requirements: Do They Match? 458 Gregor Lomas & Kelvin Mills Primary School Teachers' Perceptions of Mathematical Reasoning 466 Esther Yook-Kin Loong, Colleen Vale, Leicha Bragg & Sandra Herbert Pre-Service Teachers' Pedagogical Content Knowledge: Implications for teaching 474 Margaret Marshman & Glorianne Porter Does an Ability to Pattern Indicate That Our Thinking is Mathematical? 482 Catherine McCluskey, Michael Mitchelmore & Joanne Mulligan When a Mathematics Support Pilot Program Fails Miserably: Looking For Answers 490 Keith McNaught Student Preferences in the Design of Worked Solutions in Undergraduate Mathematics 498 David Mendiolea Using Semiotic Resources to Build Images When Teaching the Part-Whole Model of Fractions 506 Paula Mildenhall Insight into Subtraction from Large-Scale Assessment Data 514 Patricia Morley Students' Use of Online Mathematical Resources 522 Tracey Muir Tracking Structural Development Through Data Modelling in Highly Able Grade 1 Students 530 Joanne Mulligan, Kerry Hodge, Michael Mitchelmore & Lyn English Young Children Talking in Mathematics: What is the Point of That? 538 Carol Murphy How Pre-Service Teachers Integrate Knowledge of Students' Difficulties in Understanding the Concept of the Arithmetic Mean Into Their Pedagogy 546 Theodosia Prodromou Coordination of Fractional Quantities: Cueing of Resources, Constraints, and Effect of Numeric Structure 554 Ajay Ramful & Rajeev Nenduradu Pre-Service Teachers' Understanding of Measures of Centre: When the Meaning Gets Lost? 562 Robyn Reaburn Students' Understanding of Conditional Probability on Entering University 570 Robyn Reaburn Using Tablet PCs For Active Learning: Learning From Others' Mistakes 578 Daphne Robson & Dave Kennedy Entering the New Frontier of Mathematics Assessment: Designing and Trialling the PVAT-O (online). 586 Angela Rogers Overcoming Challenges of Being an In-Field Mathematics Teacher in Indigenous Secondary School Classrooms 594 Satwant Sandhu, Gillian Kidman & Tom Cooper What Financial Dilemmas Reveal About Students' Social and Mathematical Understandings 602 Carly Sawatzki iPads: Improving Numeracy Learning in the Early Years 610 Peta Spencer Classroom Culture, Challenging Mathematical Tasks and Student Persistence 618 Peter Sullivan, Amanda Aulert, Alli Lehmann, Brendan Hislop, Owen Shepherd & Alan Stubbs Teachers' Decisions About Mathematics Tasks When Planning 626 Peter Sullivan, David Clarke, Doug Clarke & Anne Roche Students Understanding of Everyday English and Kimberley Kriol in Mathematics Classroom 634 Kaye Treacy PCK and Average 642 Jane Watson & Rosemary Callingham The Influence of Mathematical Beliefs on Low-Achieving Adult Learners 650 Damon Whitten High Performance, Confidence and Disinclination to Explore: A Case Study 658 Gaye Williams Mature Age Pre-Service Teachers Mathematics Anxiety and Factors Impacting on University Retention 666 Sue Wilson Mathematics Networks and Curriculum Concepts 674 Geoff Woolcott Pre-Service Teachers' Concept Image for Circle and Ellipse 682 Vince Wright Constructing a Frame of Cube: Connecting 3D Shapes with Direction, Location and Movement 690 Andy Yeh SYMPOSIA Learning the Work of Ambitious Mathematics Teaching 699 Glenda Anthony & Roberta Hunter Using Instructional Activities to Learn the Work of Ambitious Mathematics in Pre-service Teacher Education Settings 703 Roberta Hunter, Jodie Hunter& Glenda Anthony Coaching Pre-service Teachers for Teaching Mathematics: The Views of Students 707 Robin Averill, Michael Drake & Roger Harvey Implementing the Japanese Problem-Solving Lesson Structure 711 Susie Groves Mathematical Tasks and Learning Goals: Examples from Japanese Lesson Study 715 Brian Doig Primary teachers algebraic thinking: Example from Lesson Study 719 Colleen Vale Creating Teacher Communities of Inquiry through Lesson Study 723 Wanty Widjaja Four Factors to Consider in Helping Low Achievers in Mathematics 727 Leong Yew Hoong ,Tay Eng Guan & Yap Sook Fwe Helping Low Achievers develop a Problem Solving Disposition 731 Quek Khiok Seng, Yap Sook Fwe & Tong Cherng Luen Positive Feelings towards the learning of Mathematics for low achievers 735 Tong Cherng Luen, Leong Yew Hoong & Quek Khiok Seng The Odd Couple: The Australian NAPLAN and Singaporean PSLE 739 Jane Greenlees The Classic Word Problem: The Influence of Direct Teaching 743 Tracy Logan & Siew Yin Ho Students Performance on a Symmetry Task 747 Siew Yin Ho & Tracy Logan Cross-Country Comparisons of Student Sense Making: The Development of a Mathematics Processing Framework 751 Tom Lowrie Inquiry-Based Learning in Mathematics: Designing Collaborative Research with Schools 755 Katie Makar & Shelley Dole Achievements and Challenges Encountered by Classroom Teachers Involved in a Research Project: A Reflection 759 Sue Allmond & Karen Huntly Guided Inquiry as a Model for Curriculum Resources in Mathematics 763 Christine Debritz & Rhonda Horne Building Relationships Between State Stakeholders and Researchers: People, Persistence and Passion 767 Rhonda Horne & Katie Makar Noticing Young Childrens Mathematical Strengths and Agency 771 Sue Dockett & Wendy Goff Researchers Noticing Young Childrens Mathematics 775 Barbara Clarke Visual Stimuli that Prompt Young Children to Notice their Mathematical Thinking: Two Researchers Experiences 779 Amy MacDonald & Jill Cheeseman Preschool and School Educators Noticing Young Childrens Mathematics 783 Bob Perry Learning from the Implementers in a Design Experiment 787 Toh Tin Lam, Dindyal Jaguthsing & Tay Eng Guan Fine-tuning in a Design Experiment 791 Ho Foo Him, Toh Pee Choon & Toh Tin Lam Scaffolding Cards: A Strategy for Facilitating Groups in Problem Solving 795 Toh Pee Choon, Dindyal Jaguthsing & Ho Foo Him ROUND TABLE DISCUSSIONS - Abstract only Are We Bored Yet?: Raising Attainment And Maintaining Interest Kim Beswick & Rhonda Faragher The Australian Curriculum: Mathematics (Australian Curriculum, Assessment and Reporting Authority, 2012), with its specification of content for year levels, represents a break from stage based curricula which have become the norm in Australian educational jurisdictions in recent decades. It thus provides an opportunity to rethink the appropriateness of developmental approaches to mathematics teaching and the concept of readiness that underpins the widely accepted tenet of teaching from where students are at (Anderson, 2010). Such an approach has the risk of students who fall behind their peers remaining behind even when they make progress (Capraro, Young, Lewis, Yetkiner, & Woods, 2009). This is exacerbated in mathematics because of a prevailing belief that mathematics, to a greater extent than other school subjects, is inherently hierarchical and hence must be taught in a linear fashion that precludes access to advanced content (e.g., algebra) until more basic topics (e.g., arithmetic) have been mastered. A year level based mathematics curriculum has the potential to contribute to solving at least two major problems that currently characterise mathematics learning particularly in the middle and secondary years of schooling. These are 1) persistent gaps in attainment between various disadvantaged groups and a majority of their year level peers, and 2) impoverished curriculum offerings for low attaining students who struggle to master 'basic' content. This Roundtable will provide a forum for discussion of these propositions and the opportunity afforded by the implementation of the year level based Australian Curriculum: Mathematics. Stimulus in the form of evidence that challenges the hierarchical and linear nature of mathematics learning will presented and ways that these ideas might contribute to closing attainment gaps discussed. Assessment Standards In Undergraduate Mathematics Carmel Coady, Deborah King & Cristina Varsavsky This roundtable will report and seek participants feedback on progress towards the project Developing a shared understanding of assessment criteria and standards for undergraduate mathematics, funded by the Office of Learning and Teaching. The project seeks to engage the higher education mathematics community in a conversation around assessment standards which builds upon the Learning and Teaching Academic Standards project outcomes for the sciences (Yates, Jones & Kelder, 2011), and their contextualisation within the mathematics discipline. It aims to influence assessment practices in mathematics departments, to move away from idiosyncratic marking and grading approaches that favour procedural mastery towards practices that measure the quality of all aspects of student work against external anchors, ensuring comparability of standards within and across mathematics departments. The project will result in a reference framework and toolkit to support tertiary educators in the development of quality assessment standards and criteria. The project approach incorporates the four essential elements that, according to Sadler (2009), are required to convey and apply achievement standards: (i) exemplars of different levels of achievement invoking the criteria relevant to the judgment made, each of them with an (ii) explanation of how the judgment was made; a (iii) conversation about the exemplars and their corresponding judgments to establish a common vocabulary; and (iv) the sharing of what has been tacit knowledge within the discipline community. Accelerated Learning in Mathematics Fiona Fox & Komathi Kolandai-Matchett What is acceleration and how do we achieve it? Effective classroom pedagogy occurs in classrooms where the teacher has evidence of accelerating the progress of priority group learners. Accelerated Learning in Mathematics (ALiM) is a national intervention introduced in New Zealand in 2010 aimed at accelerating the learning of those students below and well-below national expectations. It focuses on the expertise within the school to evaluate the effectiveness of current practices that support accelerated mathematics learning and to closely monitor the impact of a 10 -15 week intervention for a small group of students. The attention is on supporting teachers and schools to inquire into how an effective teacher provides a short and intensive supplementary programme alongside their classroom programme to accelerate progress. The key themes for teaching are accelerated learning; pedagogical response to individual learning strengths and needs; carefully designed mathematics task in response to identity, language and culture; genuine engagement with parents and family; collaborative inquiry; and high levels of teacher reflective practice. In this round table presentation we will present findings from schools who participated in this intervention in 2012. We will examine the main focus for teaching these students and the impact this intervention had on the rest of the school. We will look at how these schools engaged the parent/family and what effect this had on the rate of acceleration. Finally we will analyse to what extent the teachers were engaged into inquiring into their own teaching practice and to what extent this impacted on the learning of the students. Teacher Judgements in Mathematics Christine Hardie National Standards, introduced into New Zealand schools in 2010, require teachers in years one to eight to make overall teacher judgments in mathematics. This new assessment policy asks teachers to use the standards and exemplars to make defensible and dependable holistic judgments about whether a student is above, at, below or well below their year standard. The centrality, complexity and nature of teacher judgment practice in mathematics in such a policy context need to be understood. My study drew from principals and teachers perspectives about how teachers approach and make overall teacher judgments in mathematics and was gathered using semi-structured interviews and from document analysis. Participants included four principals and seven teachers of students in years three to six. A range of approaches to judgment making emerged from exploring the beliefs, understandings and judgment practices teachers adopted. Teachers utilised both explicit and tacit knowledge in the decision making process and valued their relationship with and knowledge of their students, giving attention to features other than those specified in the mathematics standards. This round table forum will begin with a short presentation of findings to initiate discussion regarding influences that could be considered to ensure teacher judgments in mathematics are dependable and whether exemplars and standards are sufficient to inform professional judgments in mathematics. Students' Transition From Number To Algebra Christina Lee & Christine Ormond In the 21st century algebra continues to be seen as a gatekeeper course for mathematics (Rand Mathematics Study Panel, 2003). Many future career opportunities are lost to students who do not have a good understanding of algebra at some level. The Australian Curriculum, in its strand Number and algebra, introduces formal algebra to students at an earlier stage than has been the case in most Australian states in the past. In this round table presentation we will firstly examine some aspects of what the curriculum says about early algebraic ideas and reasoning. We will then examine three lesson plans designed to introduce students to foundational algebraic concepts, also discussing some current doctoral research. This research asks: What strategies do teachers use when teaching algebra in the transition years, and how do these choices reflect their beliefs about mathematics teaching and learning? Participants will have the opportunity to discuss the results of some current research on teachers beliefs and practices in this area of teaching. They will also review some research findings in current literature, and what this says about the teaching and learning of early algebraic concepts. National Testing: Is it valid Fiona McDiarmid & Deb Gibbs The recent publication of the Trends in International Mathematics and Science Study (TIMSS) 2011, has raised much debate in the public and political arena in New Zealand. Analysis of the data indicates that New Zealand students performed less well than most developed countries, and performance of ten year olds has declined since 2001. The question being asked is, Why are New Zealands ten year olds not performing as well as those in other developed countries? In 2010, New Zealand introduced National Standards in mathematics, reading and writing. The mathematics standards rely on teachers making judgments about a students overall learning from a wide range of relevant evidence. Other countries such as Australia, England and the United States of America have introduced national testing. The notion that New Zealand students arent practised in taking tests in this manner has been offered as an explanation for the decline. How does a students prior test-taking skills and experience impact on results in such a high stakes activity? Do international tests like TIMSS provide an accurate measurement of a students mathematical understanding and ability to solve complex problems? Should teachers be investing some time in practising the techniques for tests of this type? This round table forum presents a small-scale study investigating the impact of practiced skills involved in test taking in relation to mathematics standard data. Discussion will focus on high stakes testing versus overall teacher judgments in assessing mathematical competence. SHORT COMMUNICATIONS - Abstract only Student Engagement in Mathematics: Switching Students On to Mathematics Janette Bobis, Jenni Way, Judy Anderson & Maryam Khosronejad Research indicates that students are switching-off mathematics from as early as Year 5. This presentation reports on an intervention study aimed at improving middle year students engagement in mathematics. Twenty middle year teachers and their students (N=339) from seven schools were involved in a year-long professional development program. Student motivation and engagement levels in mathematics were assessed prior to and at the completion of the intervention. Comparison of student data with those from a similar cohort not involved in the intervention indicates that it is possible to reduce, and even reverse, the downward shift in student engagement levels in mathematics. What Does Numeracy Mean to Teachers of Subjects Other Than Mathematics? Elizabeth Ferme Although there has been considerable research into the importance of teaching numeracy and being numerate, little is reported on how numeracy is regarded in the secondary school setting by non-mathematics teachers. This paper reports on a preliminary study into the prominence of numeracy in Australian curriculum documentation and teacher perceptions of numeracy in their daily practice. Results indicate that secondary teachers have a narrow view of numeracy and have limited access to professional learning in that area. How Is Teaching As Inquiry Impacted By Cross-Grouping In Mathematics? Rosemary Golds The New Zealand Curriculum advocates a reflective strategy termed teaching as inquiry, which encourages teachers to plan for their learners, then continually reflect and respond to their learners needs (Ministry of Education, 2007). The February 2013 ERO report, Mathematics in Years 4 to 8: Developing a Responsive Curriculum (Education Review Office, 2013), has questioned the ability of some schools to be able to provide a responsive mathematics curriculum, particularly for students who are under-achieving. One of the factors which may be having a negative impact on teacher ability to foster teaching as inquiry is the practice of streaming which has become quite common in recent years in New Zealand primary school mathematics (Years 1-8). This paper looks at the background of streaming in classrooms, and explores the connections that can be made with current research in regards to effective classroom practice for all learners of mathematics. "Am I a Maths Type of Person": Responses of Top Stream Year 8 Students Gavin Little As part of a longitudinal study on mathematics identity formation and senior subject selection, responses from five top streamed classes of Year 8 students, to the open-ended question Am I a maths type of person? have been thematically analysed through examination of key words. Consideration is given to the type of mathematical identity these top streamed students are constructing and how this is related to their intended mathematics pathway in Years 11 and 12. Narrative Inquiry and the Formation of Mathematics Identity Gavin Little Mathematics identity, as a specific type of identity, may be considered through a variety of paradigms. If identity is defined as a narrative, analysis of the formation of mathematics identity may be undertaken through narrative inquiry. A narrative approach allows the researcher to consider both personal understandings and meanings relating to mathematics identity, in the participants spatial and temporal location. Narrative inquiry allows the consideration of the why behind participants statements and actions, within their particular context, over a period of time. Utilizing Open-Source Dynamic Mathematics Software in Teaching Geometry: an Mailizar This paper discusses the differences of students achievement between using open-source dynamic mathematics software (GeoGebra) and Geometers Sketchpad in learning geometry. There were 43 participants taken from two secondary school classes in Indonesia. The GeoGebra group consists of 21 students, and the Geometers Sketchpad group consists of 22 students. The findings show that the use dynamic mathematics software can have positive effect on students achievement. However, findings do not show any significant difference between the two groups. Impact on Identity and Self-Efficacy of Primary Pre-Service Teachers: Experiences In the Mathematics Practicum Classroom Karen McDaid Developing quality teachers of mathematics is a global concern and research into mathematics teaching, early career primary teacher identity and teacher self-efficacy often focused on teachers beliefs and the relationship between beliefs and teaching practice. While some studies have looked at early career teachers and mathematics, none have focused solely on pre-service teacher beliefs about their teaching identity as teachers of primary mathematics as it is constructed over the duration of the practicum. The proposed longitudinal case study aims to track the impact on self-efficacy and identity of pre-service primary teachers as they participate in their practice teaching. Worksheets vs. Practical Activities in Mathematics in the Primary Classroom Bilinda Offen As a teacher educator in primary mathematics, I am intrigued by the number of worksheets used; this is the antithesis of my philosophy of how primary mathematics should be implemented. My proposed research is informed by a study by Marcia L. Tate (2009). My study will compare the engagement of students, concept retention and practical application of numeracy skills of children using worksheets to those involved in practical hands on activities. The children will be taught using a range of activities. Their learning behaviours will be monitored, they will be interviewed regarding their attitudes and formative assessment will be administered. The Implementation of the Patterns and Early Algebra Preschool (PEAP) Professional Development (PD) Program in Indigenous Communities across New South Wales Marina Papic, Kate Highfield, Joanne Mulligan, Judith McKay-Tempest, Deborah Garret, Monique Mandarakas, & Elizabeth Granite This short communication outlines a three-year study with 15 Aboriginal Community Childrens Services across New South Wales and the Australian Capital Territory. The project engaged more than 60 early childhood educators and approximately 240 children aged 4 to 5 years. Following an Early Mathematical Patterning Assessment (Papic, in press; Papic, Mulligan, & Mitchelmore, 2011) the project implemented an early patterning framework that developed young children's mathematical thinking and problem-solving skills. Follow up interviews with kindergarten teachers, supported by data from Best Start assessments (NSW Department of Education & Training, 2009), provides evidence of the potential impact of this program on childrens mathematics learning. A key finding is the increased confidence and pedagogical content knowledge of early childhood educators. "Teacher's Dilemma" In Using The Internet As A Mathematical Resource In Multilingual Settings Sitti Maesuri Patahuddin Indonesian government policy stipulating English as the language of mathematics instruction has created dilemmas for mathematics teachers since they are themselves not proficient in English communication, or with the English mathematics register. The question thus arose as to how mathematics online learning resources (in English) could support the development of learners English Maths proficiency. Would the language in which mathematical ideas are communicated deny learners access to mathematics learning and constrain teachers capacity to develop rich mathematical talk? Both questions will be discussed through critical incidents from video data analysis of one teacher, teaching fractions in a secondary school. Mentoring Undergraduate Primary Education Students In The Mathematics Classroom ? The Development Of A New Model To Help Reduce Mathematics Anxiety Timothy Perkins Increasing numbers of students enrolled in primary pre-service teacher Education degrees in Australia enter university with insufficient mathematical content knowledge (Livy & Vale, 2011) and low confidence levels about their ability to teach and do the mathematics required for their intended role as classroom teachers (Wilson, 2009). Teachers need to have the knowledge and teaching skills to improve student outcomes in the mathematics field (Beswick, 2012). This research project explores the development of a mentoring model aimed at increasing the confidence and competence of pre-service primary teachers by matching them with well trained, highly capable, confident and supportive primary mathematics teachers as mentors. Students' Preferences When Learning How To Use Advanced Calculators To Solve Mathematics Problems Hazel Tan In this presentation findings from part of a PhD study on students learning preferences and their use of advanced calculators such as graphics calculators and CAS calculators will be shared. Students responses to a question asking for their preferred method of learning how to use the calculators to solve mathematics problems will be shared. Amongst the different methods, the highest percentage of students indicated that they most preferred to try out the calculator steps while receiving instructions such as observing a demonstration, listening to an explanation, or reading the instructions. The implications of the findings will be discussed. POSTERS Abstract only Investigating the effect of the second-order use of context on Mathematics literacy tasks Felipe Almuna-Salgado & Caroline Bardini The incorporation of contextualised tasks has been highly recommended by reform documents and curricula. Nevertheless, the role that task context plays in assessments is an unsolved matter because there are arguments relate to whether it makes a task easier or harder for students. This study represents an attempt to scrutinise to what extent the nature of demand of the second-order use of context may affect students performance on literacy tasks. It is anticipated that this study can provide a deeper understanding of how task context impacts students performance, thereby contributing to the improvement of contextualised assessments among teachers, policy makers, and assessment writers. Exploring secondary school mathematics teachers understanding of statistical graphs Ajeevsing Bholoa & Leena Ramkalawon One of the most basic tasks in statistics is to represent data graphically and this suggests that teachers need to possess graphical competence. We explore the statistical graph comprehension of one pre-service and one in-service secondary school mathematics teachers through a series of video recorded interviews. Initially, both teachers claimed strong self-efficacy towards teaching statistical graphs conceptually. However, thinking processes deployed by them to selected statistical tasks revealed procedural knowledge rather than the claimed conceptual knowledge. These consequences suggest that the focus should be on developing the necessary competencies of teachers to work with statistical graphs effectively. Designing a detailed instructional framework: A teaching experiment in multiplication and division David Ellemor-Collins Within a larger design research project, we developed an instructional framework for multiplication and division, to be refined through a teaching experiment with low-attaining primary students. We describe the instruction at multiple scales, from the broad organization into domains and phases, through the sequencing of small topics, to the details of specific instructional activities. We also map the multiple dimensions of mathematisation involved: progressions toward larger numbers, more abstract settings, more formal notations, more sophisticated strategies, and so on. The framework contributes to research on arithmetic instruction; and also to our developing notions of frameworks, learning trajectories, and instructional design. Testing a Framework of Cognitive Ability and Student's Thinking Process in Geometric Argumentation Tsu-Nan Lee & Caroline Bardini This study aims to analyse students thinking process in geometric argumentation from geometric examples and counter-examples between Grade 3, 5 and 7 students in Victoria, Australia and Taiwan. There are two experiments in this study. The first will test and compare cognitive frameworks of geometric argumentation. The second will analyse students thinking process though geometric examples. It is anticipated that this study can provide a better understanding of thinking process in geometric activities and assist students enhance their abilities in geometry. Pattern-based learning in Linear Algebra Rosemarie Mohais In the traditional Mathematics classroom, usually a small fraction of students are able to form or recognise patterns which are core to solving problems, however, many other students never get as far. Pattern-based learning is a new developing strategy that aims to promote effective teaching/learning of Mathematics by enabling all students to recognise patterns. The technique involves presentation of the solutions to standard well-known problems through software. Once the student has gained experience in solving multiple problems using a clear pattern of solution, he/she can then independently apply the technique. In this poster, Pattern-based learning is applied to Linear Algebra. Effects of using different types of display and rules on pre-schoolers patterning recognition in Malaysia: A preliminary study Sharifah Norul Akmar Syed Zamri & Nor Adlina Fadil The aim of this preliminary study is to explore the effects of using different types of display and pattern rules on achievement in pattern recognition among pre-schoolers in Malaysia. A total of one hundred and fifty six pre-schoolers were involved in this study. The instrument used was adapted from Gadzichowski (2012). It contains 25 patterns which were divided into five different groups based on display; colour, shape, object, letter and number. Each group comprised five different patterns with rules of increasing difficulty. Each child was interviewed individually. A correct answer was given 1, otherwise zero. Descriptive statistics and a two factor ANOVA for correlated measures were conducted. Results show that the overall achievement of the children was rather low. Children find certain rules easier than others. The different displays had no significant impact on the achievement of pattern recognition amongst these children.


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